LB: I use an organizer in many of my larger handbags.... but especially drawstrings and bucket bags. I find that a soft sided organizer works best in handbags where the base is not a typical rectangle. The organizer makes it easier to find things because otherwise they travel over the bottom of the bag. They do make organizers that are a strip of pockets that you can curve and conform to the shape of the bottom of a handbag. Then I guess you use bigger stuff in the middle, where there is not organizer, to keep the sides standing up. I haven't tried this kind of organizer. I use a nylon/mesh organizer from Ebay. It's soft and light and can be bent to fit the bottom of the bag. Then I can put some things in the organizer and some larger items around the outside between the organizer and the sides of the bag. I find this works very well. These nylon/mesh organizers are very inexpensive and come in several sizes. I use one, but I suppose you could use 2 smaller ones in a drawstring if you liked the organization of the space better that way.
BTW, these organizers are also good in hobo bags to keep your stuff in place. Some ladies don't mind if their things travel within their handbags. I prefer to know exactly where something will be when I reach for it.
These days lots of ladies uses pouches instead of organizers. It's just a different technique. I switch depending upon the handbag design.Larger handbags will accommodate either an organizer or pouches. Smaller handbags may work better with one or the other, depending upon size and shape of the bag, the organizer, and your stuff. I find that several, smaller pouches work best in smaller handbags.